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In 2012, filmmaker Haifaa al-Mansour became the first woman to direct a feature film in Saudi Arabia when she made “Wadjda,” a terrifically entertaining movie about a girl who enters a Koran recitation competition to raise funds for a bicycle.

As a metaphor for women’s status in Saudi Arabia, “Wadjda” was both a sobering tutorial and oblique call to arms. And, over the past decade, things have genuinely changed: When she made “Wadjda,” Mansour was forced to direct from inside a van, so as not to mix with her male crew. This time, she worked freely. And her films can now be seen in movie theaters in the kingdom, where they were once banned.

Women can also drive, a development that is pointedly reflected in the opening sequence of “The Perfect Candidate,” which again finds Mansour contemplating the state of Saudi women and how far they have yet to go. As physician Maryam (Mila Alzahrani) drives to her small-town clinic, she’s first met with an almost unpassable unpaved road that mires her car and oncoming ambulances in debilitating mud. But that’s nothing compared with the sexism Maryam confronts inside the clinic, where an elderly patient refuses to look at her and demands to be treated by less qualified male nurses.

What does this have to do with political candidacy? The film gets there, after some Kafkaesque scenes of Maryam trying to travel to Dubai for a medical conference, without her father’s permission. (That rule has since been rescinded.) At first because of a clerical misunderstanding and then out of sheer determination, she decides to run for the local municipal council, with her sole campaign issue being to pave the road to the clinic.

As with “Wadjda,” Mansour gives audiences a candid, often wryly amusing glimpse of life inside the Saudi kingdom, which is so often cloaked in opacity and menace. What for many Westerners looks like an impenetrable and rigid society is revealed to be more elastic, whether for women donning and doffing their niqabs as the situation demands, or Maryam’s musician father, Abdulaziz (Khalid Abdulrahim), testing how far official Saudi culture will go in welcoming his band.

The musical interludes of Abdulaziz’s oud-playing are among the most gratifying in “The Perfect Candidate,” as are some spectacular wedding sequences. Alzahrani is joined by Dhay and Nora al-Awad as Maryam’s sisters Selma and Sara; the three create a thoroughly convincing chemistry as young women navigating bureaucratic and theological thickets in their own individually subversive ways. (For Maryam, her political career has nothing to do with feminism or “women’s issues,” a theoretical construct her opponents simply can’t grasp.)

“The Perfect Candidate” includes at least one or two triumphant scenes, when Maryam’s impatience with patriarchal hostility finally bursts forth. But some quieter moments are even more meaningful. “I’ll show them what I’m made of, and they’ll give me a better position,” Maryam says to Selma when she decides to run for office. To which her sister carefully replies: “I’m not sure that’s how it works.”

Unrated. At the Angelika Pop-Up and Angelika Film Center Mosaic. Contains some smoking. In Arabic with subtitles. 105 minutes.